TL;DRAbstract
Considerable attention has recently been devoted to the representation for offset curves.Farouki and Sakkalis studied a class of curves called Pythagorean hodograph curves (PH curves), which have rationally parameterized offsets. Lu proved that for a planar cubic parametric curve which has no cusps and is not a PH curve, its offset curve is not a (piecewise) rational curve. In this note, we give a sufficient and necessary characterization to describe such a set of curves whose offsets can be expressible as piecewise rational curves.
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Considerable attention has recently been devoted to the representation for offset curves.Farouki and Sakkalis studied a class of curves called Pythagorean hodograph curves (PH curves), which have rationally parameterized offsets. Lu proved that for a planar cubic parametric curve which has no cusps and is not a PH curve, its offset curve is not a (piecewise) rational curve. In this note, we give a sufficient and necessary characterization to describe such a set of curves whose offsets can be expressible as piecewise rational curves.
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